Neutral differential equations find numerous applications in natural science and technology. For instance, they are frequently used for the study of distributed networks containing lossless transmission lines; see Hale 1 . In recent years, many studies have been made on the oscillatory behavior of solutions of neutral delay differential equations, and we refer to the recent papers 2–23 and the ...

Abstract In this paper, we are concerned with the convergence rate of Euler–Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) neutral type , where neutral, drift, and diffusion terms allowed to be polynomial growth. More precisely, SDDEs driven by Brownian motions, reveal that corresponding EM is one-half; Whereas pure jump processes, show best associated slower than one-...

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov-Razumikhin technique for neutral equations with finite del...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of ...

Abstract We consider the approximate controllability for a class of second-order impulsive neutral stochastic differential equations with state-dependent delay and Poisson jumps in real separable Hilbert space. Under sufficient conditions, we obtain results by virtue theory strongly continuous cosine family bounded linear operators combined inequality technique Sadovskii fixed point theorem. Fi...